It's unlikely to company will pay for damages to your vehicle because, as you stated, you misjudged where the gate would open to. In terms of filing a claim with your insurance company, I recommend getting an estimate first to see how much the damage will cost. Especially because this type of claim would be considered a collision
claim, which can impact your premium going forward. If the damages aren't too expensive, you're probably better off paying for it out of pocket.